%I #11 Dec 02 2022 16:42:33
%S 2,6,10,18,38,84,186,410,904,1994,4398,9700,21394,47186,104072,229538,
%T 506262,1116596,2462730,5431722,11980040,26422810,58277342,128534724,
%U 283492258,625261858,1379058440,3041609138,6708480134,14796018708,32633646554,71975773242
%N Number of fault-free tilings of a 4 X 2n rectangle with L tetrominoes.
%C Fault-free tilings are those where the only straight interface is at the left and right end. Thus a(n) <= A084480(n).
%C If the conjectured G.F. in A183304 is true, then a(n)= 2*A183304(n-1), n>3. - _R. J. Mathar_, Dec 02 2022
%H Colin Barker, <a href="/A084481/b084481.txt">Table of n, a(n) for n = 1..1000</a>
%H C. Moore, <a href="http://arXiv.org/abs/math.CO/9905012">[math/9905012] Some Polyomino Tilings of the Plane</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,0,1).
%F G.f.: 2*z*(1+z)^2*(1-z-z^3) / (1-2*z-z^3).
%F a(n) = 2*a(n-1) + a(n-3) for n>6. - _Colin Barker_, Mar 28 2017
%o (PARI) Vec(2*x*(1 + x)^2*(1 - x - x^3) / (1 - 2*x - x^3) + O(x^30)) \\ _Colin Barker_, Mar 28 2017
%Y Cf. A084478, A084479, A084480, A084477.
%K nonn,easy
%O 1,1
%A _Ralf Stephan_, May 27 2003